In this paper, we studied theoretically the surface heat transmission by natural convection in turbulent boundary layer from the vertical flat plate to the surrounding fluid. For this purpose, we paid attention to the laminar sublayer that exists near the surface and brings very great thermal resistance on the surface heat transmission. Now we assume that in the laminar sublayer, the following relation exists, [numerical formula] where δ
s is the thickness of the laminar sublayer, and T
1, T
s and T
0 are the absolute temperatures of the surface of plate, the surface of laminar sublayer and the surrounding gas, respectively, g is acceleration due to gravity, ν is kinematic viscosity of fluid and P
r is Prandtl number, and G is a constant. Using this assumption as the basis of theoretical analysis, we obtained the next relation among non-dimensional numbers, that is, N
um=0°251P
0.3rG
0.3r where N
um is Nusselt number and G
r is Grashoff number. Our theoretical results agree very well with the results which many investigators have already obtained by experiments. And we found that the constant G is about 200.
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